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Quantifying passing skill has been a topic that has gained greater attention over the past 18 months in public analytics circles, with Paul Riley, StatsBomb and Played off the Park regularly publishing insights from their passing models. I talked a little about my own model last season but only published results on how teams disrupted their opponents passing. I thought delving into the nuts and bolts of the model plus reporting some player-centric results would be a good place to start as I plan to write more on passing over the next few months.

Firstly, the model quantifies the difficulty of an open-play pass based on its start and end location, as well as whether it was with the foot or head. So for example, relatively short backward passes by a centre back to their goalkeeper are completed close to 100% of the time, whereas medium-range forward passes from out-wide into the centre of the penalty area have pass completion rates of around 20%.

The data used for the model is split into training and testing sets to prevent over-fitting. The Random Forest-based model does a pretty good job of representing the different components that drive pass difficulty, some of which are illustrated in the figure below (also see the appendix here for some further diagnostics).

Comparison between expected pass completion rates from two different passing models and actual pass completion rates based on the start and end location of an open-play pass. The horizontal dimension is orientated from left-to-right, with zero designating the centre of the pitch. The dashed lines in the vertical dimension plots show the location of the edge of each penalty area. Data via Opta.

One slight wrinkle with the model is that it has trouble with very short passes of less than approximately 5 yards due to the way the data is collected; if a player attempts a pass and an opponent in his immediate vicinity blocks it, then the pass is unsuccessful and makes it looks like such passes are really hard, even though the player was actually attempting a much longer pass. Neil Charles reported something similar in his OptaPro Forum presentation in 2017. For the rest of the analysis, such passes are excluded.

None shall pass

That gets some of the under-the-hood stuff out of the way, so let’s take a look at ways of quantifying passing ‘skill’.

Similar to the concept of expected goals, the passing model provides a numerical likelihood of a given pass being completed by an average player; deviations from this expectation in reality may point to players with greater or less ‘skill’ at passing. The analogous concept from expected goals would be comparing the number of goals scored versus expectation and interpreting this as ‘finishing skill‘ or lack there of. However, when it comes to goal-scoring, such interpretations tend to be very uncertain due to significant sample size issues because shots and goals are relatively infrequent occurrences. This is less of a concern when it comes to passing though, as many players will often attempt more passes in a season than they would take shots in their entire career.

Another basic output of such models is an indication of how adventurous a player is in their passing – are they playing lots of simple sideways passes or are they regularly attempting defense-splitting passes?

The figure below gives a broad overview of these concepts for out-field players from the top-five leagues (England, France, Germany, Italy and Spain) over the past two seasons. Only passes with the feet are included in the analysis.

Passing ‘skill’ compared to pass difficulty for outfield players from the past two seasons in the big-five leagues, with each data point representing a player who played more than 3420 minutes (equivalent to 38 matches) over the period. The dashed lines indicate the average values across each position. Foot-passes only. Data from Opta.

One of the things that is clear when examining the data is that pulling things apart by position is important as the model misses some contextual factors and player roles obviously vary a huge amount depending on their position. The points in the figure are coloured according to basic position profiles (I could be more nuanced here but I’ll keep it simpler for now), with the dashed lines showing the averages for each position.

In terms of pass difficulty, midfielders attempt the easiest passes with an average expected completion of 83.2%. Forwards (81.6%) attempt slightly easier passes than defenders (81.4%), which makes sense to me when compared to midfielders, as the former are often going for tough passes in the final third, while the latter are playing more long passes and crosses.

Looking at passing skill is interesting, as it suggest that the average defender is actually more skilled than the average midfielder?!? While the modern game requires defenders to be adept in possession, I’m unconvinced that their passing skills outstrip midfielders. What I suspect is happening is that passes by defenders are being rated as slightly harder than they are in reality due to the model not knowing about defensive pressure, which on average will be less for defenders than midfielders.

Forwards are rated worst in terms of passing skill, which is probably again a function of the lack of defensive pressure included as a variable, as well as other skills being more-valued for forwards than passing e.g. goal-scoring, dribbling, aerial-ability.

Pass muster

Now we’ve got all that out of the way, here are some lists separated by position. I don’t watch anywhere near as much football as I once did, so really can’t comment on quite a few of these and am open to feedback.

Note the differences between the players on these top-ten lists are tiny, so the order is pretty arbitrary and there are lots of other players that the model thinks are great passers who just missed the cut.

First-up, defenders: *shrugs*.

In terms of how I would frame this, I wouldn’t say ‘Faouzi Ghoulam is the best passer out of defenders in the big-five leagues’. Instead I would go for something along the lines of ‘Faouzi Ghoulam’s passing stands out and he is among the best left-backs according to the model’. The latter is more consistent with how football is talked about in a ‘normal’ environment, while also being a more faithful presentation of the model.

Looking at the whole list, there is quite a range of pass difficulty, with full-backs tending to play more difficult passes (passes into the final third, crosses into the penalty area) and the model clearly rates good-crossers like Ghoulam, Baines and Valencia. Obviously that is a very different skill-set to what you would look for in a centre back, so filtering the data more finely is an obvious next step.

Defenders (* denotes harder than average passes)

Name

Team

xP rating

Pass difficulty

Faouzi Ghoulam

Napoli

1.06

80.3*

Leighton Baines

Everton

1.06

76.5*

Stefan Radu

Lazio

1.06

82.1

Thiago Silva

PSG

1.06

91.0

Benjamin Hübner

Hoffenheim

1.05

84.4

Mats Hummels

Bayern Munich

1.05

86.0

Kevin Vogt

Hoffenheim

1.05

87.4

César Azpilicueta

Chelsea

1.05

83.4

Kalidou Koulibaly

Napoli

1.05

87.8

Antonio Valencia

Manchester United

1.05

80.0*

On to midfielders: I think this looks pretty reasonable with some well-known gifted passers making up the list, although I’m a little dubious about Dembélé and Fernandinho being quite this high up. Iwobi is an interesting one and will keep James Yorke happy.

Fàbregas stands-out due to his pass difficulty being well-below average without having a cross-heavy profile – nobody gets near him for the volume of difficult passes he completes.

Midfielders (* denotes harder than average passes)

Name

Team

xP rating

Pass difficulty

Cesc Fàbregas

Chelsea

1.06

79.8*

Toni Kroos

Real Madrid

1.06

88.1

Luka Modric

Real Madrid

1.06

85.9

Arjen Robben

Bayern Munich

1.05

79.6*

Jorginho

Napoli

1.05

86.8

Mousa Dembélé

Tottenham Hotspur

1.05

89.9

Fernandinho

Manchester City

1.05

87.2

Marco Verratti

PSG

1.05

87.3

Alex Iwobi

Arsenal

1.05

84.9

Juan Mata

Manchester United

1.05

84.5

Finally, forwards AKA ‘phew, it thinks Messi is amazing’.

Özil is the highest-rated player across the dataset, which is driven by his ability to retain possession and create in the final third. Like Fàbregas above, Messi stands out for the difficulty of the passes he attempts and that he is operating in the congested central and half-spaces in the final third, where mere mortals (and the model) tend to struggle.

In terms of surprising names: Alejandro Gomez appears to be very good at crossing, while City’s meep-meep wide forwards being so far up the list makes we wonder about team-effects.

Also, I miss Philippe Coutinho.

Forwards (* denotes harder than average passes)

Name

Team

xP rating

Pass difficulty

Mesut Özil

Arsenal

1.07

82.9

Eden Hazard

Chelsea

1.05

81.9

Lionel Messi

Barcelona

1.05

79.4*

Philippe Coutinho

Liverpool

1.04

80.6*

Paulo Dybala

Juventus

1.03

84.8

Alejandro Gomez

Atalanta

1.03

74.4*

Raheem Sterling

Manchester City

1.03

81.6*

Leroy Sané

Manchester City

1.03

81.9

Lorenzo Insigne

Napoli

1.03

84.3

Diego Perotti

Roma

1.02

78.4*

Finally, the answer to what everyone really wants to know is, who is the worst passer? Step-forward Mario Gómez – I guess he made the right call when he pitched his tent in the heart of the penalty area.

Pass it on

While this kind of analysis can’t replace detailed video and live scouting for an individual, I think it can provide a lot of value. Traditional methods can’t watch every pass by every player across a league but data like this can. However, there is certaintly a lot of room for improvement and further analysis.

A few things I particularly want to work on are:

Currently there is no information in the model about the type of attacking move that is taking place, which could clearly influence pass difficulty e.g. a pass during a counter-attacking situation or one within a long passing-chain with much slower build-up. Even if you didn’t include such parameters in the model, it would be a nice means of filtering different pass situations.

Another element in terms of context is attempting a pass after a dribble, especially given some of the ratings above e.g. Hazard and Dembélé. I can envisage the model somewhat conflates the ability to create space through dribbling and passing skill (although this isn’t necessarily a bad thing depending on what you want to assess).

Average difficulty is a bit of a blunt metric and hides a lot of information. Developing this area should be a priority for more detailed analysis as I think building a profile of a player’s passing tendencies would be a powerful tool.

You’ll have probably noticed the absence of goalkeepers in the results above. I’ve left them alone for now as the analysis tends to assign very high skill levels to some goalkeepers, especially those attempting lots of long passes. My suspicion is that long balls up-field that are successfully headed by a goalkeeper’s team-mate are receiving a bit too much credit i.e. yes the pass was ‘successful’ but that doesn’t always mean that possession was retained after the initial header. That isn’t necessarily the fault of the goalkeeper, who is generally adhering to the tactics of their team and the match situation but I’m not sure it really reflects what we envisage as passing ‘skill’ when it comes to goalkeepers. Discriminating between passes to feet and aerial balls would be a useful addition to the analysis here.

Using minutes as the cut-off for the skill ratings leaves a lot of information on the table. The best and worst passers can be pretty reliably separated after just a few hundred passes e.g. Ruben Loftus-Cheek shows up as an excellent passer after just ~2000 minutes in the Premier League. Being able to quickly assess young players and new signings should be possible. Taking into account the number of passes a player makes should also be used to assess the uncertainty in the ratings.

I’ve gone on enough about this, so I’ll finish by saying that any feedback on the analysis and ratings is welcome. To facilitate that, I’ve built a Tableau dashboard that you can mess around with that is available from here and you can find the raw data here.

Goalkeepers have typically been a tough nut to crack from a data analytics point-of-view. Randomness is an inherent aspect of goal-scoring, particularly over small samples, which makes drawing robust conclusions at best challenging and at worst foolhardy. Are we identifying skill in our ratings or are we just being sent down the proverbial garden path by variance?

To investigate some of these issues, I’ve built an expected save model that takes into account shot location and angle, whether the shot is a header or not and shot placement. So a shot taken centrally in the penalty area sailing into the top-corner will be unlikely to be saved, while a long-range shot straight at the keeper in the centre of goal should usually prove easier to handle.

The model is built using data from the past four seasons of the English, Spanish, German and Italian top leagues. Penalties are excluded from the analysis.

The model thus provides an expected goal value for each shot that a goalkeeper faces, which we can then compare with the actual outcome. In a simpler world, we could easily identify shot-stopping skill by taking the difference between reality and expectation and then ranking goalkeepers by who has the best (or worst) difference.

However, this isn’t a simple world, so we run into problems like those illustrated in the graphic below.

Each individual red marker is a player’s shot-stopper rating over the past four seasons versus the number of shots they’ve faced. We see that for low shot totals, there is a huge range in the shot-stopper-ranking but that the spread decreases as the number of shots increases, which is an example of regression to the mean.

To illustrate this further, I used a technique called boot-strapping to re-sample the data and generate confidence intervals for an average goalkeeper. This re-sampling is done 10,000 times to create a probability distribution built by randomly extracting groups of shots from the data-set and calculating actual and expected save percentages and then seeing how large the difference is. We see a strong narrowing of the blue uncertainty envelope up to around 50 shots, with further narrowing up to about 200 shots. After this, the narrowing is less steep.

What this effectively means is that there is a large band of possible outcomes that we can’t realistically separate from noise for an average goalkeeper. Over a season, a goalkeeper faces a little over 100 shots on target (119 on average according to the data used here). Thus, there is a huge opportunity for randomness to play a role and it is therefore of little surprise to find that there is little repeatability year-on-year for save percentage.

Things do start to settle down as shot totals increase though. After 200 shots, a goalkeeper would need to be performing more than ± 4% on the shot-stopper-rating scale to stand up to a reasonable level of statistical significance. After 400 shots, signal is easier to discern with a keeper needing to register more than ± 2% to emerge from the noise. That is not to say that we should be beholden to statistical significance but it is certainly worth bearing in mind in any assessment plus an understanding of the uncertainty inherent in analytics can be a powerful weapon to wield.

What we do see in the graphic above are many goalkeepers outside of the blue uncertainty envelope. This suggests that we might be able to identify keepers who are performing better or worse than the average goalkeeper, which would be pretty handy for player assessment purposes. Luckily, we can employ some more maths courtesy of Pete Owen who presented a binomial method to rank shot-stopping performance in a series of posts available here and here.

The table below lists the top-10 goalkeepers who have faced more than 200 shots over the past four seasons by the binomial ranking method.

I don’t know about you but that doesn’t look like too shabby a list of the top keepers. It may be that some of the names on the list have serious flaws in their game aside from shot-stopping but that will have to wait another day and another analysis.

So where does that leave us in terms of goalkeeping analytics? On one hand, we have noisy unrepeatable metrics from season-to-season. On the other, we appear to have some methods available to extract the signal from the noise over larger samples. Even then, we might be being fooled by aspects not included in the model or the simple fact that we expect to observe outliers.

Deficiencies in the model are likely our primary concern but these should be checked by a skilled eye and video clips, which should already be part of the review process (quit sniggering at the back there). Consequently, the risks ingrained in using an imperfect model can be at least partially mitigated against.

Requiring 2-3 seasons of data to get a truly robust view on shot-stopping ability may be too long in some cases. However, perhaps we can afford to take a longer-term view for such an important position that doesn’t typically see too much turnover of personnel compared to other positions. The level of confidence you might want when short-listing might well depend on the situation at hand; perhaps an 80% chance of your target being an above average shot-stopper would be palatable in some cases?

All this is to say that I think you can assess goalkeepers by the saves they do or do not make. You just need to be willing to embrace a little uncertainty in the process.

Identifying scoring talent is one of the main areas of investigation in analytics circles, with the information provided potentially helping to inform decisions that can cost many, many millions. Players who can consistently put the ball in the net cost a premium; can we separate these players from the their peers?

I’m using data from the 2008/09 to 2012/13 seasons across the top divisions in England, Spain, Germany and Italy from ESPN. An example of the data provided is available here for Liverpool in 2012/13. This gives me total shots (including blocked shots) and goals for over 8000 individual player seasons. I’ve also taken out penalties from the shot and goal totals using data from TransferMarkt. This should give us a good baseline for what looks good, bad and extraordinary in terms of scoring talent. Clearly this ignores the now substantial work being done in relation to shot location and different types of shot but the upside here is that the sample size (number of shots) is larger.

Below is a graph of shot conversion (defined as goals divided by total shots) against total shots. All of the metrics I’ll use will have penalties removed from the sample. The average conversion rate across the whole sample is 9.2%. Using this average, we can calculate the bounds of what average looks like in terms of shot conversion; we would expect some level of random variation around the average and for this variation to be larger for players who’ve taken fewer shots.

Shot conversion versus total shots for individual players in the top leagues in England, Italy, Spain and Germany from 2008/09-2012/13. Points are shown in grey with certain players highlighted, with the colours corresponding to the season. The solid black line is the average conversion rate of 9.2%, with the dotted lines above and below this line corresponding to two standard errors above the average. The dashed line corresponds to five standard errors. Click on the image for a larger view.

On the plot I’ve also added some lines to illustrate this. The solid black line is the average shot conversion rate, while the two dotted lines either side of it represent upper and lower confidence limits calculated as being two standard errors from the mean. These are known as funnel plots and as far as I’m aware, they were introduced to football analysis by James Grayson in his work on penalties. Paul Riley has also used them when looking at shot conversion from different areas of the pitch. There is a third dotted line but I’ll talk about that later.

So what does this tell us? Well we would expect approximately 95% of the points to fall within this envelope around the average conversion rate; the actual number of points is 97%. From a statistical point of view, we can’t identify whether these players are anything other than average at shot conversion. Some players fall below the lower bound, which suggests that they are below average at converting their shots into goals. On the other hand, those players falling above the upper bound, are potentially above average.

The Bad

I’m not sure if this is surprising or not, but it is actually quite hard to identify players who fall below the lower bound and qualify as “bad”. A player needs to take about 40 shots without scoring to fall beneath the lower bound, so I suspect “bad” shooters don’t get the opportunity to approach statistical significance. Some do though.

Only 62 player seasons fall below the lower bound, with Alessandro Diamanti, Antonio Candreva, Gökhan Inler and (drum-roll) Stewart Downing having the dubious record of appearing twice. Downing actually holds the record in my data for the most shots (80) without scoring in 2008/09, with his 2011/12 season coming in second with 71 shots without scoring.

The Good

Over a single season of shots, it is somewhat easier to identify “good” players in the sample, with 219 players lying above the two standard error curve. Some of these players are highlighted in the graph above and rather than list all of them, I’ll focus on players that have managed to consistently finish their shooting opportunities at an above average rate.

Only two players appear in each of the five seasons of this sample; Gonzalo Higuaín and Lionel Messi. Higuaín has scored an impressive 94 goals with a shot conversion rate of 25.4% over that sample. I’ll leave Messi’s numbers until a little later. Four players appear on four separate occasions; Álvaro Negredo, Stefan Kießling, Alberto Gilardino and Giampaolo Pazzini. Negredo is interesting here as while his 15.1% conversion rate over multiple seasons isn’t as exceptional as some other players, he has done this over a sustained period while taking a decent volume of shots each season (note his current conversion rate at Manchester City is 16.1%).

Eighteen players have appeared on this list three times; notable names include van Persie, Di Natale, Cavani, Agüero, Gómez, Soldado, Benzema, Raúl, Fletcher, Hernández and Agbonlahor (wasn’t expecting that last one). I would say that most of the players mentioned here are more penalty box strikers, which suggests they take more of their shots from closer to the goal, where conversion rates are higher. It would be interesting to cross-check these with analysts who are tracking player shot locations.

The Messi

To some extent, looking at players that lie two standard errors above or below the average shot conversion rate is somewhat arbitrary. The number of standard errors you use to judge a particular property typically depends on your application and how “sure” you want to be that the signal you are observing is “real” rather than due to “chance”. For instance, when scientists at CERN were attempting to establish the existence of the Higgs boson, they used a very stringent requirement that the observed signal is five standard errors above the typical baseline of their instruments; they want to be really sure that they’ve established the existence of a new particle. The tolerance here is that there be much less than a one in a million chance that any observed signal be the result of a statistical fluctuation.

As far as shot conversion is concerned, over the two seasons prior to this, Lional Messi is the Higgs boson of football. While other players have had shot conversion rates above this five-standard error level, Messi has done this while taking huge shot volumes. This sets him apart from his peers. Over the five seasons prior to this, Messi took 764 shots, from which an average player would be expected to score between 54 and 86 goals based on a player falling within two standard errors of the average; Messi has scored 162! Turns out Messi is good at the football…who knew?

This is a short follow-up to this post using the same dataset. Instead of shot conversion, we’re now looking at shooting accuracy which is defined as the number of shots on target divided by the total number of shots. The short story here is that shooting accuracy regresses more strongly to the mean than shot conversion at the larger shot samples (more than 70 shots) and is very similar below this.

Comparison between shooting accuracy for players in year zero and the following season (year one). Click on the image or here for a larger interactive version.

Minimum Shots

Players

year-to-year r^2

‘luck’

‘skill’

1

2301

0.045

79%

21%

10

1865

0.118

66%

34%

20

1428

0.159

60%

40%

30

951

0.214

54%

46%

40

632

0.225

53%

47%

50

456

0.219

53%

47%

60

311

0.190

56%

44%

70

180

0.245

51%

49%

80

117

0.305

45%

55%

90

75

0.341

42%

58%

100

43

0.359

40%

60%

Comparison of the level of ‘skill’ and ‘luck’ attributed to shooting accuracy (measured by shots on target divided by all shots) from one season to the next. The data is filtered by the total number of shots a player takes in consecutive seasons.

Essentially, there is quite a bit of luck involved with getting shots on target and for large-volume shooters, there is more luck involved in getting accurate shots in than in scoring them.

In my previous post (many moons ago), I looked at whether a players’ shot conversion in one season was a good guide to their shot conversion in the next. While there were some interesting features in this, I was wary of being too definitive given the relatively small sample size that was used. Data analysis is a journey with no end, so this is the next step. I collated the last 5 seasons of data across the top divisions in England, Spain, Germany and Italy (I drew the line at collecting France) from ESPN. An example of the data provided is available here for Liverpool in 2012/13. The last 5 seasons on ESPN are Opta provided data and matched up perfectly when I compared with English Premier League data from EPL-Index.

Before digging into the results, a few notes on the data. The data is all shots and all goals i.e. penalties are not removed. Ideally, you would strip out penalty shots and goals but that would require player-level data that I don’t have and I’ve already done enough copy and pasting. I doubt including penalties will change the story too much but it would alter the absolute numbers. Shot conversion here is defined as goals divided by total shots, where total shots includes blocked shots. I then compared shot conversion for individual players in year zero with their shot conversion the following year (year one). The initial filter that I applied here was that the player had to have scored at least one goal in both years (so as to exclude players having 0% shot conversion).

Comparison between shot conversion rates for players in year zero and the following season (year one). Click on the image or here for a larger interactive version.

Starting out with the full dataset, we have 2301 data points where a player scored a goal in two consecutive seasons. The R^2 here (a measure of the strength of the relationship) is very low, with a value of 0.061 (where zero would mean no relationship and one would be perfect). Based on the method outlined here by James Grayson, this suggests that shot conversion regresses 75% towards the mean from one season to the next. The implication of this number is that shot conversion is 25% ‘skill’ and 75% is due to random variation, which is often described as ‘luck’.

As I noted in my previous post on this subject, the attribution to skill and luck is dependent on the number of shots taken. As the number of shots increases, we smooth out some of the randomness and skill begins to emerge. A visualisation of the relationship between shot conversion and total shots is available here. Below is a summary table showing how this evolves in 10 shot increments. After around 30 shots, skill and luck are basically equal and this is maintained up to 60 shots. Above 80 shots, we seem to plateau at a 70/30% split between ‘skill’ and ‘luck’ respectively.

Minimum Shots

Players

year-to-year r^2

‘luck’

‘skill’

1

2301

0.061

75%

25%

10

1865

0.128

64%

36%

20

1428

0.174

58%

42%

30

951

0.234

52%

48%

40

632

0.261

49%

51%

50

456

0.262

49%

51%

60

311

0.261

49%

51%

70

180

0.375

39%

61%

80

117

0.489

30%

70%

90

75

0.472

31%

69%

100

43

0.465

32%

68%

Comparison of the level of ‘skill’ and ‘luck’ attributed to scoring ability (measured by shot conversion) from one season to the next. The data is filtered by the total number of shots a player takes in consecutive seasons.

The results here are different to my previous post, where the equivalence of luck and skill was hit around 70 shots whereas it lies from 30-60 shots here. I suspect this is driven by the smaller sample size in the previous analysis. The song remains the same though; judging a player on around half a season of shots will be about as good as a coin toss. Really you want to assess a heavy shooter over at least a season with the proviso that there is still plenty of room for random variation in their shot conversion.

What is shot conversion anyway?

The past summer in the football analytics community saw a wonderful catalytic cycle of hypothesis, analysis and discussion. It’s been great to see the community feeding off each other; I would have liked to join in more but the academic conference season and the first UK heatwave in 7 years put paid to that. Much of the focus has been on shots and their outcomes. Increasingly the data is becoming more granular; soon we’ll know how many shots per game are taken within 10 yards of the corner flag at a tied game state by players with brown hair and blue eyes while their manager juggles on the sideline (corrected for strength of opposition of course). This increasing granularity is a fascinating and exciting development. While it was already clear that all shots aren’t created equal from purely watching the football, the past summer has quantified this very clearly. To me, this demonstrates that the traditional view of ‘shot conversion’ as a measure of finishing ability is erroneous.

As an illustrative example, consider two players who both take 66 shots in a season. Player A scores 11 goals, so has a shot conversion of 17%. Player B scores 2 goals, so has a shot conversion of 3%. The traditional view of shot conversion would suggest that Player A is a better finisher than Player B. However, if Player A took all of his shots from a central area within the 18-yard box, he would be bang in line with the Premier League average over the past 3 seasons. If Player B took all of his shots from outside the area, he would also be consistent with the average Premier League player. Both players are average when controlling for shot location. Clearly this is an extreme example but then again it is meant to be an illustration. To me at least, shot conversion seems more indicative of shooting efficiency i.e. taking shots from good positions under less defensive pressure will lead to an increased shot conversion percentage. Worth bearing in mind the next time someone mentions ‘best’ or ‘worst’ in combination with shot conversion.

The remaining question for me is how sustainable the more granular data is from season-to-season, especially given the smaller sample sizes.

With the football season now over across the major European leagues, analysis and discussion turns to reflection of the who, what and why of the past year. With the transfer window soon to do whatever the opposite of slam shut is, thoughts also turn to how such reflections might inform potential transfer acquisitions. As outlined by Gabriele Marcottitoday in the Wall Street Journal, strikers are still the centre of attention when it comes to transfers:

The game’s obsession with centerforwards is not new. After all, it’s the glamour role. Little kids generally dream of being the guy banging in the goals, not the one keeping them out.

On the football analytics front, there has been a lot of discussion surrounding the relative merits of various forward players, with an increasing focus on their goal scoring efficiency (or shot conversion rate) and where players are shooting from. There has been a lot of great work produced but a very simple question has been nagging away at me:

Does being ‘good’ one year suggest that you’ll be ‘good’ next year?

We can all point to examples of forwards shining brightly for a short period during which they plunder a large number of goals, only to then fade away as regression to their (much lower) mean skill level ensues. With this in mind, let’s take a look at some data.

Scoring proficiency

I’ve put together data on players over the past two seasons who have scored at least 10 goals during a single season in the top division in either England, Spain, Germany or Italy from WhoScored. Choosing 10 goals is basically arbitrary but I wanted a reasonable number of goals so that calculated conversion rates didn’t oscillate too wildly and 10 seems like a good target for your budding goalscorer. So for example, Gareth Bale is included as he scored 21 in 2012/13 and 9 goals in 2011/12 but Nikica Jelavić isn’t as he didn’t pass 10 league goals in either season. Collecting the data is painful so a line had to be drawn somewhere. I could have based it on shots per game but that is prone to the wild shooting of the likes of Adel Taarabt and you end up with big outliers. If a player was transferred to or from a league within the WhoScored database (so including France), I retained the player for analysis but if they left the ‘Big 5’ then they were booted out.

In the end I ended up with 115 players who had scored at least 10 league goals in one of the past two seasons. Only 43 players managed to score 10 league goals in both 2011/12 and 2012/13, with only 6 players not named Lionel Messi or Cristiano Ronaldo able to score 20 or more in both seasons. Below is how they match up when comparing their shot conversion, where their goals are divided by their total shots, across both seasons. The conversion rates are based on all goals and all shots, ideally you would take out penalties but that takes time to collate and I doubt it will make much difference to the conclusions.

Comparison between shot conversion rates for players in 2011/12 and 2012/13. Click on the image or here for a larger interactive version.

If we look at the whole dataset, we get a very weak relationship between shot conversion in 2013/12 relative to shot conversion in 2011/12. The R^2 here is 0.11, which suggests that shot conversion by an individual player shows 67% regression to the mean from one season to the next. The upshot of this is that shot conversion above or below the mean is around two-thirds due to luck and one-third due to skill. Without filtering the data any further, this would suggest that predicting how a player will convert their chances next season based on the last will be very difficult.

A potential issue here is the sample size for the number of shots taken by an individual in a season. Dimitar Berbatov’s conversion rate of 44% in 2011/12 is for only 16 shots; he’s good but not that good. If we filter for the number of shots, we can take out some of the outliers and hopefully retain a representative sample. Up to 50 shots, we’re still seeing a 65% regression to the mean and we’ve reduced our sample to 72 players. It is only when we get up to 70 shots and down to 44 players that we see a close to even split between ‘luck’ and ‘skill’ (54% regression to the mean). The problem here is that we’re in danger of ‘over-fitting’ as we rapidly reduce our sample size. If you are happy with a sample of 18 players, then you need to see around 90 shots per season to able to attribute 80% of shot conversion to ‘skill’.

Born again

So where does that leave us? Perhaps unsurprisingly, the results here for players are similar to what James Grayson found at the team level, with a 61% regression to the mean from season to season. Mark Taylor found that around 45 shots was where skill overtook luck for assessing goal scoring, so a little lower than what I found above although I suspect this is due to Mark’s work being based on a larger sample over 3 season in the Premier League.

The above also points to the ongoing importance of sample size when judging players, although I’d want to do some more work on this before being too definitive. Judgements on around half a season of shots appears rather unwise and is about as good as flipping a coin. Really you want around a season for a fuller judgement and even then you might be a little wary of spending too much cash. For something approaching a guarantee, you want some heavy shooting across two seasons, which allied with a good conversion rate can bring you over 20 league goals in a season. I guess that is why the likes of Van Persie, Falcao, Lewandowski, Cavani and Ibrahimovic go for such hefty transfer fees.

Passing network for Barcelona and AC Milan from the Champions League match at the Camp Nou on the 12th March 2013. Only completed passes are shown. Darker and thicker arrows indicate more passes between each player. The player markers are sized according to their passing influence, the larger the marker, the greater their influence. The size and colour of the markers is relative to the players on their own team i.e. they are on different scales for each team. Only the starting eleven is shown. Click on the image for a larger view.

I’ve previously looked at whether different playing styles can be assessed using seasonal data for the 2011/12 season. The piece concentrated on whether it was possible to separate different playing styles using a method called Principal Component Analysis (PCA). At a broad level, it was possible to separate teams between those that were proactive and reactive with the ball (Principal Component 1) and those that attempted to regain the ball more quickly when out of possession (Principal Component 2). What I didn’t touch upon was whether such features were potentially more successful than others…

Below is the relationship between points won during the 2011/12 season and the proactive/reactive principal component. The relationship between these variables suggests that more proactive teams, that tend to control the game in terms of possession and shots, are more successful. However, the converse could also be true to an extent in that successful teams might have more of the ball and thus have more shots and concede fewer. Either way, the relationship here is relatively strong, with an R2 value of 0.61.

Relationship between number of points won in the 2011/12 season with principal component 1, which relates to the proactive or reactive nature of a team. More proactive teams are to the right of the horizontal axis, while more reactive teams are to the left of the horizontal axis. The data is based on the teams in the top division in Germany, England, Spain, France and Italy from WhoScored. The black line is the linear trend between the two variables. A larger interactive version of the plot is available either by clicking on the graph or clicking here.

Looking at the second principal component, there is basically no relationship at all with points won last season, with an R2 value of a whopping 0.0012. The trend line on the graph is about as flat as a pint of lager in a chain sports bar. There is a hint of a trend when looking at the English and French leagues individually but the sample sizes are small here, so I wouldn’t get too excited yet.

Playing style is important then?

It’s always tempting when looking at scatter plots with nice trend lines and reasonable R2 values to reach very steadfast conclusions without considering the data in more detail. This is likely an issue here as one of the major drivers of the ‘proactive/reactive’ principal component is the number of shots attempted and conceded by a team, which is often summarised as a differential or ratio. James Grayson has shown many times how Total Shots Ratio (TSR, the ratio of total shots for/(total shots for+total shots against)) is related to the skill of a football team and it’s ability to turn that control of a game into success over a season. That certainly appears to play a roll here, as this graph demonstrates, as the relationship between points and TSR yields an R2 value of 0.59. For comparison, the relationship between points and short passes per game yields an R2 value of 0.52. As one would expect based on the PCA results and this previous analysis, TSR and short passes per game are correlated also (R2 = 0.58).

Circular argument

As ever, it is difficult to pin down cause and effect when assessing data. This is particularly true in football when using seasonal averaged statistics as score effects likely play a significant role here in determining the final totals and relationships. Furthermore, the input data for the PCA is quite limited and would be improved with more context. However, the analysis does hint at more proactive styles of play being more successful; it is a challenge to ascribe how much of this is cause and how much is effect.

Danny Blanchflower summed up his footballing philosophy with this quote:

The great fallacy is that the game is first and last about winning. It is nothing of the kind. The game is about glory, it is about doing things in style and with a flourish, about going out and beating the other lot, not waiting for them to die of boredom.

The question is, is the glory defined by the style or does the style define the glory?

The perceived playing style of a football team is a much debated topic with conversations often revolving around whether a particular style is “good/bad” or “entertaining/boring”. Such perceptions are usually based upon subjective criteria and personal opinions. The question is whether the playing style of a team can be assessed using data to categorise and compare different teams.

WhoScored report several variables (e.g. data on passing, shooting, tackling) for the teams in the top league in England, Spain, Italy, Germany and France. I’ve collated these variables for last season (2011/12) in order to examine whether they can be used to assess the playing style of these sides. In total there are 15 variables, which are somewhat limited in scope but should serve as a starting point for such an analysis. Goals scored or conceded are not included as the interest here is how teams actually play, rather than how it necessarily translates into goals. The first step is to combine the data in some form in order to simplify their interpretation.

Principal Component Analysis

One method for exploring datasets with multiple variables is Principal Component Analysis (PCA), which is a mathematical technique that attempts to find the most common patterns within a dataset. Such patterns are known as ‘principal components’, which describe a certain amount of the variability in the overall dataset. These principal components are numbered according to the amount of variance in the dataset that they account for. Generally this means that only the first few principal components are examined as they account for the greatest percentage variance in the dataset. Furthermore, the object is to simplify the dataset so examining a large number of principal components would somewhat negate the point of the analysis.

The video below gives a good explanation of how PCA might be applied to an everyday object.

Below is a graph showing the first and second principal components plotted against each other. Each data point represents a single team from each of the top leagues in England, Spain, Italy, Germany and Italy. The question though is what do each of these principal components represent and what can they tell us about the football teams included in the analysis?

Principal component analysis of all teams in the top division in England, Spain, Italy, Germany and France. Input variables are taken from WhoScored.com for the 2011/12 season.

The first principal component accounts for 37% of the variance in the dataset, which means that just over a third of the spread in the data is described by this component. This component is represented predominantly by data relating to shooting and passing, which can be seen in the graph below. Passing accuracy and the average number of short passes attempted per game are both strongly negatively-correlated (r=-0.93 for both) with this principal component, which suggests that teams positioned closer to the bottom of the graph retain possession more and attempt more short passes; unsurprisingly Barcelona are at the extreme end here. Total shots per game and total shots on target per game are also strongly negatively-correlated (r=-0.88 for both) with the first principal component. Attempted through-balls per game are also negatively correlated (r=-0.62). In contrast, total shots conceded per game and total aerial duels won per game are positively-correlated (r=0.65 & 0.59 respectively). So in summary, teams towards the top of the graph typically concede more shots and win more aerial duels, while as you move down the graph, teams attempt more short passes with greater accuracy and have more attempts at goal.

The first principal component is reminiscent of a relationship that I’ve written about previously, where the ratio of shots attempted:conceded was well correlated with the number of short passes per game. This could be interpreted as a measure of how “proactive” a team is with the ball in terms of passing and how this transfers to a large number of shots on goal, while also conceding fewer shots. Such teams tend to have a greater passing accuracy also. These teams tend to control the game in terms of possession and shots.

The second principal component accounts for a further 18% of the variance in the dataset [by convention the principal components are numbered according to the amount of variance described]. This component is positively correlated with tackles (0.77), interceptions (0.52), fouls won (0.68), fouls conceded (0.74), attempted dribbles (0.59) and offsides won (0.63). In essence, teams further to the right of the graph attempt more tackles, interceptions and dribbles which unsurprisingly leads to more fouls taking place during their matches.

The second principal component appears to relate to changes in possession or possession duels, although the data only relates to attempted tackles, so there isn’t any information on how successful these are and whether possession is retained. Without more detail, it’s difficult to sum up what this component represents but we can describe the characteristics of teams and leagues in relation to this component.

The first and second components together account for 55% of the variance in the dataset. Adding more and more components to the solution would drive this figure upwards but in ever diminishing amounts e.g. the third component accounts for 8% and the fourth accounts for 7%. For simplicity and due to the further components adding little further interpretative value, the analysis is limited to just the first two components.

Assessing team playing styles

So what do these principal components mean and how can we use them to interpret team styles of play? Putting all of the above together, we can see that there are significant differences between teams within single leagues and when comparing all five as a whole.

Within the English league, there is a distinct separation between more proactive sides (Liverpool, Spurs, Chelsea, Manchester United, Arsenal and Manchester City) and the rest of the league. Swansea are somewhat atypical, falling between the more reactive English teams and the proactive 6 mentioned previously. Stoke could be classed as the most “reactive” side in the league based on this measure.

There isn’t a particularly large range in the second principal component for the English sides, probably due the multiple correlations embedded within this component. One interesting aspect is how all of the English teams are clustered to the left of the second principal component, which suggests that English teams attempt fewer tackles, make fewer interceptions and win/concede fewer fouls compared with the rest of Europe. Inspection of the raw data supports this. This contrasts with the clichéd blood and thunder approach associated with football in England, whereby crunching tackles fly in and new foreign players struggle to adapt to the intense tackling approach. No doubt there is more subtlety inherent in this area and the current analysis doesn’t include anything about the types of tackles/interceptions/fouls, where on the pitch they occur or who perpetrates them but this is an interesting feature pointed out by the analysis worthy of further exploration in the future.

The substantial gulf in quality between the top two sides in La Liga from the rest is well documented but this analysis shows how much they differed in style with the rest of the league last season. Real Madrid and Barcelona have more of the ball, take more shots and concede far fewer shots compared with their Spanish peers. However, in terms of style, La Liga is split into three groups: Barcelona, Real Madrid and the rest. PCA is very good at evaluating differences in a dataset and with this in mind we could describe Barcelona as the most “different” football team in these five leagues. Based on the first principal component, Barcelona are the most proactive team in terms of possession and this translates to their ratio of shots attempted:conceded; no team conceded fewer shots than Barcelona last season. This is combined with their pressing style without the ball, as they attempt more tackles and interceptions relative to many of their peers across Europe.

Teams from the Bundesliga are predominantly grouped to the right-hand-side of the second principal component, which suggests that teams in Germany are keen to regain possession relative to the other leagues analysed. The Spanish, Italian and French tend to fall between the two extremes of the German and English teams in terms of this component.

All models are wrong, but some are useful

The interpretation of the dataset is the major challenge here; Principal Component Analysis is purely a mathematical construct that doesn’t know anything about football! While the initial results presented here show potential, the analysis could be significantly improved with more granular data. For example, the second principal component could be improved by including information on where the tackles and interceptions are being attempted. Do teams in England sit back more compared with German teams? Does this explain the lower number of tackles/interceptions in England relative to other leagues? Furthermore, the passing and shooting variables could be improved with more context; where are the passes and shots being attempted?

The results are encouraging here in a broad sense – Barcelona do play a different style compared with Stoke and they are not at all like Swansea! There are many interesting features within the analysis, which are worthy of further investigation. This analysis has concentrated on the contrasts between different teams, rather than whether one style is more successful or “better” than another (the subject of a future post?). With that in mind, I’ll finish with this quote from Andrés Iniesta from his interview with Sid Lowe for the Guardian from the weekend.

…the football that Spain and Barcelona play is not the only kind of football there is. Counter-attacking football, for example, has just as much merit. The way Barcelona play and the way Spain play isn’t the only way. Different styles make this such a wonderful sport.